Place fish in a well-greased large skillet. Pour milk over fish. Cover; bring to a boil. Reduce heat; simmer 8 minutes or until fish flakes easily when tested with a fork. Remove to a serving platter; keep warm. Reserve milk in skillet.
Combine butter, flour, mustard, and pepper. Add to hot milk; cook over medium heat, stirring constantly, until thickened and bubbly. Add egg, parsley, and salt, mixing well. Pour sauce over warm fish; sprinkle with paprika.